1. Field of Invention
This invention relates to determination of dynamic moves of the manipulated variables in a model predictive controller, specifically to as it relates to the method of calculation in which the steady state optimization and the dynamic moves calculation are done simultaneously as part of one optimization solution.
2. Background of the Invention
Since its inception in early 1980, the basic formulation of Model Predictive Control (MPC) has involved a two-step method of solution. The first step of constrained steady state optimization solution involves determination of optimal steady targets for both the controlled variables and the manipulated variables based on the currently predicted future steady state as per the effects of past-manipulated variables moves. The second step of the solution of dynamic move calculation in which the dynamic moves of the manipulated variables are calculated so as to derive the process to the optimal steady state targets. However, the dynamic moves are calculated as unconstrained least square solution to minimize the square of the predicted error of the controlled variables over a prediction horizon by a number of future-moves in the manipulated variables over a control horizon or some variation of this but not as explicit constrained dynamic solution. Further, by adopting a receding horizon method, both these two-steps of solution are performed repeatedly to continually update both the optimal steady state targets and the dynamic moves. One of the key deficiencies of this 2-step solution is that dynamically the controlled variables values can violate their high/low limits even though the steady state solution does not. The dynamic move calculation being an unconstrained solution does not ensure that the controlled variables do not violate their respective high/low limits while moving towards the steady state targets as determined earlier by the steady state optimization step. Consequently, in the prior art MPC, dynamic performance of a MPC can drastically change under changing process condition circumstances. Furthermore, any attempt to improve the poor performance under a set of process condition would necessitate say a change in the controller tuning, which may subsequently produce poor performance under some other process condition. The prior art MPC are not robust in their performance to a wide range of operating conditions.
In practice, to circumvent this, various forms of tuning weights for both the controlled variables and the manipulated variables are used. Particularly, for the dynamic move calculation, controlled variables weights and manipulated variables weights are required to ensure that the dynamic violations of the controlled variables are minimized. Typically, increasing manipulated variables weights reduce the dynamic violation of the controlled variables by reducing the size of the move and thus slowing down the rate of approaching the optimal steady state targets. A certain amount of tuning weights of the manipulated variables is essential to maintain dynamic stability of the process under control. However, in practice the effectiveness of the tuning weights is rather limited and very much dependent on the range of operation. One set of tuning weights values cannot ensure that dynamic violation of the controlled variables will be the same under changing operation conditions. In practice, therefore, the tuning weights are set based on a compromise whereby the dynamic violation of the controlled variables is achieved by accepting sluggish process performance. Therefore, to maintain the responsiveness and the stability of the process under control, the tuning weights are required to be adjusted from time to time. It is a trial and error method. A poorly tuned MPC would perform with excessive dynamic violation of the controlled variables under changing disturbance conditions. In a modest size MPC, it is not easy to set the tuning weights that would perform consistently at all times. Intrinsically, the 2-step method of solution of the prior art includes what can be characterized as a positive feedback loop of the effect of the unconstrained dynamic move on the steady state optimization and vice versa. This makes the prior art MPC more vulnerable to self-induced instability due to certain amount of dynamic changes in measured and unmeasured disturbances including the tuning weights of both the controlled variables and the manipulated variables.
This 2-step method of solution has been the bulwark of the MPC implementation in the industry over last 25 years. From its first introduction in early 1980 at Shell Development Company to this day, the method of solution remains basically the same. The prior art patent, U.S. Pat. No. 5,758,047 by Lu et al relates to a 2-step solution in which the dynamic moves are solved in second step by way of an augmented problem in which the first step steady state targets and the dynamic moves calculation are harmonized. Basically, Morshedi et al disclose the same 2-step process of calculation relating to dynamic moves in another earlier U.S. Pat. No. 4,616,308.